Experimental and theoretical investigation of effects of wall’s thermophysical properties on time lag and decrement factor

Energy and Buildings 34 (2002) 273±278

Experimental and theoretical investigation of effects of wall's thermophysical properties on time lag and decrement factor Koray Ulgen Solar Energy Institute, Ege University, 35100 Bornova Izmir, Turkey Received 22 May 2001; accepted 2 June 2001

Abstract Energy saving policies are necessary to control energy consumption, use energy ef®ciently and effectively, and reassess available production and consumption systems. In this context, the objectives of this study are to investigate the thermal behaviours of opaque wall materials under solar energy change, and the interaction between thermophysical characteristics of opaque wall materials and solar energy falling onto exterior surface of the wall affects interior environment. Parameters of characteristics used in wall formation, their positions, wall thermal behaviours, and ``time lag'' and ``decrement factor'' having effect on the changes of conditions of interior space were investigated experimentally for different wall formations. The experimental ®ndings were compared with the results of equations derived by using an analytic methodology. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Thermophysical properties; Time lag; Decrement factor; Sol±air temperature

1. Introduction Fossil fuel consumption in buildings to provide comfort conditions destroy ecological balance and environmental pollution endangers life. In order to minimise this negative impact, it is inevitable to higher the level of renewable energy sources usage. It is also very essential to take new measures to use more renewable energy sources in order to minimise this negative impact. Solar energy is a clean and renewable energy source, creating no waste. Climatisation of buildings could be managed by passive and active solar systems. Active systems need heat transfer and store ¯uids, control and transfer elements in order to collect and store solar energy. Building components in passive systems collect and transfer heat. Massive building elements such as walls and ¯oors work as thermal masses. Solar energy storage in sunny periods is used to heat building spaces when needed [1±3]. Daily temperature pro®le changes inside opaque wall elements can be observed depending on the temperature difference internal space and the environment. The absorption

Abbreviations: VCbrick, vertical cavernous brick; HCbrick, horizontal cavernous brick; Cbrick, coat brick; TCbrick, thin coat brick; EPfoam, extrude polystren foam; Ppanel, prefabricated panel; Styrofoam, expanded polystren foam; Kapipane, permeable insulation material E-mail address: [email protected] (K. Ulgen).

of solar radiation from the external opaque wall causes a gradual rise in the temperature distribution through the wall until an equilibrium state is being reached. This process is called the thermal inertia of the internal space and wall system [4,5]. On this transient period, temperature pro®le on the wall cross-section has been assumed to be sinusoidal wave. This observed change depending on thermophysical properties, and on the inner side of wall, it reaches the lowest level sinusoidal change in reaching from outside to inner face de®ned as time lag or phase lag (f). Lowering entity of amplitude is de®ned as decrement factor and attenuation factor (f) [6]. A schematic of time lag and decrement factor are shown in Fig. 1. Depending on the thermophysical properties and thickness of opaque wall elements, approximately 12 h time lag values can be observed. So, passive energy storage applications during the day can be also used at night. Further, the decrease in the indoor temperatures can be prevented when the heating system was switched off. In hot and arid climate zones using specially designed walls, the variation of the outdoor temperatures has a very little effect on the indoor temperature [7]. The heat ¯ux within the envelope of the building occurs in the transient regime under the effect of solar radiation. Various analytical and numerical methods have been developed for the solution of the differential equation, which represents this form of the heat transfer [8±14].

0378-7788/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 7 7 8 8 ( 0 1 ) 0 0 0 8 7 - 1

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K. Ulgen / Energy and Buildings 34 (2002) 273±278

Nomenclature

k P R S t T w x

thermal diffusivity (m2 s 1) amplitude specific heat (kJ kg 1 K 1) decrement factor experimental decrement factor theoretical decrement factor convective heat transfer coefficient (W m 2 K 1) total solar radition for vertical surface (W m 2) thermal conductivity (W m 1 K 1) period (24 h) thermal resistance (W 1 m2 K) heat storage capacity (W s1/2 m 2 K 1) time (h) temperature (8C) angular speed (rad s 1) thickness (m)

Greek letters a b f fexperiment ftheoric r

absorptivity surface tilt angles (8) time lag (h) experimental time lag theoretical time lag mass density (kg m 3)

Subscripts a,in a,out in out sa s,i s,o

indoor amplitude outdoor amplitude indoor outdoor sol±air indoor surface outdoor surface

a A c f fexperiment ftheoric h I

In this study, the behaviour of opaque wall materials constituting building surfaces under solar energy is investigated both experimentally and theoretically in order to ®nd time lag and decrement factor for different wall compositions. The main aim in doing this study is to determine proper wall compositions used in passive solar buildings. 2. Analysis In this study, in order to obtain the theoretical results of opaque wall systems studied, it is assumed that wall elements have a ®nite length, and one-dimensional transient heat conduction through the wall. One-dimensional transient heat conduction equation is as follows: rc

@T @2T ˆk 2: @t @x

(1)

The Fourier equation describes the temperature at a point in the wall and at some instant. To solve Eq. (1), it is necessary to specify an initial condition and two boundary conditions. The boundary condition at the exterior surface is   @T k ˆ hout …Tsa Tout †: (2) @x xˆ0 Eq. (2) includes the gain due to the absorbed incident solar radiation for the exterior surface of the opaque wall and the heat loss by convection to the ambient air from the exterior surface. Similarly, the boundary condition at the interior surface can be written as   @T k ˆ hin …Ts;i Tin †: (3) @x xˆL The first term of Eq. (3) represents the conduction heat transfer through the wall, while the second term represents the convective heat transfer between the interior surface of the opaque wall and the indoor air. The temperature values at the time t ˆ 0 can be taken as initial condition. For the

Fig. 1. The schematic representation of the time lag, f, and decrement factor, f ˆ Ain =Aout .

K. Ulgen / Energy and Buildings 34 (2002) 273±278

temperature affecting the exterior surface of the opaque wall, a theoretical temperature referring to the joint effect of the outdoor air temperature and the absorbed solar energy and indicating periodical change by time has been used. In the literature, this temperature is called sol±air temperature [9]. Tsa ˆ Tout ‡

a It hout

e DR : hout

(4)

ASHRAE recommends that the correction factor, e DR=hout , be given a value 48C for horizontal surfaces facing up. Thus, the sol±air temperature is 48C cooler due to reduced infrared radiation coming from the sky. The correction factor is specified to be 0 for vertical surfaces, as the warmer sunlit surfaces compensate for the cooler sky temperature. An estimate of the correction factor for other tilt angles based upon radiation shape-factor geometry is e DR ˆ 4 cos b; (5) hout where b is the surface tilt angles measured between the surfaces normal and vertical [9]. Under the initial and boundary conditions given above, the following Eq. (6) can be obtained from the solution of the equation of heat conduction, which is one-dimensional and dependent on time: q T…x; t† ˆ X12 ‡ X22 ‰sin…wt ‡ f†Š: (6) Eq. (6) is the analytical solution to the problem. X1 and X2 are function of x and can be calculated from the following equations:

275

3. Experimental studies Based on the earlier studies given in the literature, the experimental set-up whose subsections are given below has been developed in this study [15]. It is aimed at determining the behaviour of the envelope of the building under the effect of solar radiation [16]:    

simulation unit; datalogger (for storing data and controlling the system); computer (for organising the data stored); temperature sensors (used for measuring wall surface and environment temperatures);  test samples (wall structures to be tested and having 1 m  1 m surface area on each side). The simulation unit shown schematically in Fig. 2 consists of three parts. The space A represents the environment, and the temperature change in the space A is assumed to be sinusoidal. A heating unit, a cooling unit and fan are placed inside the space A. The goal is to create a sinusoidal temperature change by changing the energy level at certain time intervals, keeping the energy level by which is given heater and cooler into the volume ®xed (Fig. 3a). In order for periodical change to have some time intervals, simulation time is taken as 32 h. First 2 h are the time elapsed for the system to reach equilibrium; the last 30 h are a change process having ®ve periods to reach the steady state regime. Each period represents a day. Measurements are made to determine how periodical temperature change, simulated in the space A, is re¯ected into the space B (Fig. 3b). In the wall part, there are 10 wall samples, which form the context of

"

# p p p …hin =S i †sinh‰…S i =k†…L x†Š ‡ cosh‰…S i =k†…L x†Š p p p p X1 ˆ Ta;out ; ……S i =hout † ‡ …hin =S i ††sinh……S i =k†L† ‡ …1 ‡ …hin =hout ††cosh……S i =k†L† " # p p p …hin =S i †sinh……S i =k†x† ‡ …hin =hout †cosh……S i =k†x† p p p p X2 ˆ Ta;in ; ……S i =hout † ‡ …hin =S i ††sinh……S i =k†L† ‡ …1 ‡ …hin =hout ††cosh……S i =k†L†

Sˆ

p rck:

(9)

At the same time, the ratio of X1 to X2 gives the time lag between interior and exterior surfaces of the opaque element.   X2 f ˆ arctan : (10) X1 In addition, the square-rooted term of Eq. (6) refers to the reduction in the amplitude of the surface temperatures, which is decrement factor. q (11) f ˆ X12 ‡ X22 : The results of the analytical solution are given in Table 1. For the convective heat transfer coefficient values considered in analytical solutions are measured experimentally.

(7) (8)

the study and are designed for different climate conditions. These samples have 1 m  1 m surface area and are insulated from the side surfaces to realise one-dimensional heat conduction only. Datalogger unit consisted of an electronic card for generating periodical temperature changes and a storage card for receiving the signals coming from sensors during measurements. Sensors were used to measure the temperatures of the environment and wall surfaces. The sensors were produced speci®cally concerted datalogger through electronic chips. The calibration of the sensors, before each experiment, was made on the calibration card placed in datalogger unit. There were 12 sensors: two for measuring environment temperature and the rest for measuring surface temperature. Also there was transfer unit in the system to convey data collected by the datalogger to the computer. Data transfer

Fig. 2. The schematic representation of the simulation unit.

Table 1 Theoretical and experimental results Wall no.

Sheet type (out towards in)

Thickness a ˆ k/rc S ˆ (krc)1/2 (cm) (m2 s1  10 7) (W s1/2 m2 K1)

1

Outer plaster VCbrick Inner plaster

3.00 19.00 2.00

3.63 5.95 3.20

481.66 453.65 282.84

Outer plaster Gas concrete Inner plaster

3.00 20.00 2.00

3.63 3.35 3.20

481.66 242.02 282.84

Outer plaster EPfoam VCbrick Inner plaster

3.00 3.00 19.00 2.00

3.63 8.25 5.95 3.20

481.66 32.70 453.65 282.84

4

Outer plaster VCbrick EPfoam Inner plaster

3.00 19.00 3.00 2.00

3.63 5.95 8.25 3.20

481.66 453.65 32.70 282.84

5

Cbrick Air space HCbrick Inner plaster

9.00 3.00 13.50 2.00

4.93 0.02 4.10 3.20

825.88 5.61 476.24 282.84

Cbrick Ppanel HCbrick Inner plaster

9.00 3.00 13.50 2.00

4.93 18.20 4.10 3.20

825.88 29.66 476.24 282.84

7

Cbrick Air space EPfoam HCbrick Inner plaster

9.00 3.00 3.00 13.50 2.00

4.93 0.02 8.25 4.10 3.20

825.88 5.61 32.70 476.24 282.84

8

TCbrick Styrofoam HCbrick Inner plaster

1.50 2.00 13.50 2.00

6.75 8.27 4.10 3.20

1380.26 34.09 476.24 282.84

9

Outer plaster Styrophore Inner plaster

3.00 15.00 2.00

3.63 28.13 3.20

481.66 26.83 282.84

10

Cam Kapipane VCbrick Inner plaster

0.40 3.00 19.00 2.00

5.90

1151.24

5.95 3.20

453.65 282.84

2

3

6

R (W1 m2 K)

Theoretical

Experimental fexperiment

fexperiment (h)

9.39

0.392

10.50

0.690

9.42

0.375

10.27

2.861 2.099 4.125 2.392

0.529

11.48

0.357

10.10

1.7814

0.861 0.519 0.980 0.903

3.008 5.703 2.816 2.988

0.395

14.52

0.281

11.28

1.7340

0.347 0.954 0.820 0.922

5.804 2.469 4.137 1.915

0.250

14.33

0.332

11.44

1.3302

0.407 0.944 0.839 0.923

5.676 2.307 4.038 2.073

0.299

14.09

0.351

11.56

2.7441

0.351 0.925 0.970 0.826 0.923

5.782 1.702 2.718 4.110 2.056

0.240

16.37

0.243

11.58

1.0834

0.821 0.935 0.847 0.922

3.168 2.109 3.996 1.809

0.599

11.08

0.362

10.34

3.5618

0.779 0.992 0.922

2.908 2.942 3.780

0.714

9.63

0.365

10.30

1.0637

0.973 0.981 0.880 0.919

2.793 0.186 3.898 2.493

0.775

9.37

0.415

9.52

ftheoric

ftheoric (h)

2.974 4.001 2.411

0.676

1.6570

0.860 0.875 0.917

2.432 3.716 3.275

1.7814

0.835 0.935 0.744 0.912

Decrement factor, f

Time lag, f (h)

0.7713

0.863 0.855 0.913

K. Ulgen / Energy and Buildings 34 (2002) 273±278

277

Fig. 3. Internal view of (a) space A and (b) space B.

the functions of thermal diffusivity (a), mass density (r) and speci®c heat (c) of the material. Atmospheric conditions and purpose of use of spaces have some effects on passing of the heat through the wall and on storage of the heat. The walls in the study have different formations. Time lag and decrement factor values of opaque wall elements forming building shell under the periodic change conditions are illustrated in Table 1. Based on the experimental results and theoretical calculations, as seen in Table 2, the best results are obtained by using multi-layered insulated and air-cavernous wall formations (wall no.: 7), followed by insulated (interior and exterior) formations (wall nos.: 4, 5, 6, 3, 8), and single-layered formations (wall nos.: 1, 2, 9, 10). Characteristic magnitude of time lag and decrement factor that will inform the designers concerning material characteristics and their positions forming wall formations are affected by heat storage (S) and thermal diffusivity (a) of the material. The increase in both mass density and speci®c heat values has a positive effect on the results. On the contrary, increase of the thermal conductivity causes heat storage coef®cient to change positively (increase in value), but causes heat-spreading coef®cient to change negatively (increase in value). It means that it is impossible to obtain positive results for both characteristics. Thus, it is inevitable to consider composite types of walls formed by layers having different features in design for the best results. A

unit was connected to the serial port of the datalogger. A connection cable was used between the computer and the transfer unit to transfer data from the serial port. Moreover, a speci®cally produced keypad was used to enter the command. In order to determine thermophysical behaviours of opaque wall elements forming building shell under the effect of solar energy showing periodical change, thermal tests of 10 different types of walls were conducted in the experimental simulation unit developed. Building materials forming wall types and their positions are given in Table 1 [16]. 4. Results and discussion In the effective use of energy, the environmental temperature, solar radiation intensity purpose of use of spaces and characteristics, dimensions and formations of structure elements forming building shell are important parameters. The walls, which are in interaction continuously with changing environmental temperature and solar radiation, can be organised as single-layered or multi-layered in terms of their formation. As known, heat-spreading and storage features of the material gain importance in time lag, decrement factor, and magnitude of heat loss. Those features mentioned are

Table 2 The order of evaluation of wall formation tested by their theoretical experimental examinations (by wall numbers) Evaluation rank

1 2 3 4 5 6 7 8 9 10

Theoretical

Experimental

Decrement factor

Time lag

Decrement factor

Time lag

7 5 6 4 3 8 1 2 9 10

7 4 5 6 3 8 9 2 1 10

7 4 5 6 3 8 9 2 1 10

7 6 5 4 1 8 9 2 3 10

Results

Evaluation rank

7 5 4 6 3, 8 3, 8 1, 9 1, 9 2 10

1 2 3 4 5 5 7 7 9 10

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K. Ulgen / Energy and Buildings 34 (2002) 273±278

small thermal diffusivity having effects on decrement factor and increases in time lag that is a large mass density (r) and speci®c heat (c) have a positive impact on the interior environmental conditions. 5. Conclusions Appropriate building shell can be obtained with massive block having heat storage feature and composite types of walls formed by light and non-heat conducting materials, by giving attention to the function of interior space, and to the position of the material in wall formations. Utilisation period is also effective in terms of selection of opaque wall materials forming building shell. In the spaces used for short time and limited time intervals, a lower level of heat storage capacity of the building shell is preferred, while a higher level is preferred in buildings used for long periods of time. This is very essential for keeping the temperature changes of interior space at minimum level. In conclusion, many parameters should be taken into consideration for providing comfort in spaces. In the buildings used for all day long (houses, of®ces, etc.), multilayered and insulated wall formations are suggested, while single-layered formations are suggested for the buildings used for speci®c time intervals. Acknowledgements The author is grateful to the Research Fund of Ege University for substantial support in realising this study, and to the Association of Turgutlu Brick and Tile Producers for contributions in providing the experiment mechanisms to the Ege University Solar Energy Institute.

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